Module supersingulier et homologie des courbes modulaires

✍ Scribed by Marusia Rebolledo

• Book ID: 104024707
• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 277 KB
• Volume: 121
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.02.005

✦ Synopsis

We study here the free group generated by isomorphism classes of supersingular elliptic curves in positive characteristic. We compare this Z-module to the homology of the modular curve X 0 (p). We give an interpretation of Gross formula for special values of L-functions of modular forms in this context. As an application, we obtain a formula for the sum of the squares of the optimal embeddings numbers of quadratic orders in a definite quaternion algebra.